Rateless codes, and especially Raptor codes, have received considerable attention in the recent past due to their inherent ability to adapt to channel conditions and their capacity- approaching performance. Since decoding of rateless codes typically involves multiple decoding attempts, early termination of such attempts is mandatory for overall efficient decoding. In this letter, we propose a new decoding scheme with early termination that is particularly suited for rateless codes. Simulation results for the example of the binary symmetric channel show complexity reductions (in terms of the total required number of decoding iterations) by 87% compared to conventional message-passing decoding and 54% compared to a recently proposed incremental decoding scheme for Raptor codes.